Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility κT we now turn to the available numerical evidence to elucidate the character of the partial differential equation: Of the three scenarios identified previously, only the assumption of the equations turning stiff when building up the divergence of κT allo...

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equat...

Explicit stabilized methods for stiff ordinary differential equations have a long history. Proposed in the early 1960s and developed during 40 years for the integration of stiff ordinary differential equations, these methods have recently been extended to implicit-explicit or partitioned type methods for advection-diffusion-reaction problems, and to efficient explicit solvers for stiff mean-squ...

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate fractional Volterra integro-differential equation ψ-Hilfer derivative in k-normed spaces obtain approximation for this type equation.

The importance of delay differential equations (DDEs), in modelling mathematical biological, engineering and physical problems, has motivated searchers to provide efficient numerical methods for solving such important type of differential equations. Most of these types of differential models are stiff, and suitable numerical methods must be introduced to simulate the solutions. In this paper, w...

The proper modeling of nonequilibrium gas dynamics is required in certain regimes of hypersonic flow. For inviscid flow this gives a system of conservation laws coupled with source terms representing the chemistry. Often a wide range of time scales is present in the problem, leading to numerical difficulties as in stiff systems of ordinary differential equations. Stability can be achieved by us...

in previous studies we first concentrated on utilizing crisp simulationto produce discrete event fuzzy systems simulations. then we extendedthis research to the simulation of continuous fuzzy systems models. in this paperwe continue our study of continuous fuzzy systems using crisp continuoussimulation. consider a crisp continuous system whose evolution depends ondifferential equations. such a ...

In this paper, optimal control for stochastic linear singular Takagi–Sugeno (T–S) fuzzy delay system with quadratic performance is obtained using genetic programming (GP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional GP approach. The GP solution is equivale...